The 22-year-old has been ruled out for four to six weeks after rupturing ankle ligaments in last week's dramatic Europa League victory over Borussia Dortmund.
Euro 2016 begins in just over seven weeks and Can is confident that he can be fully fit in time to feature for his country.
"I am a fighter and won't let anything get me down," he told SID.
"I will give everything to try and be fit in time for the Euros and I am optimistic about achieving my goal."
Can has made five international appearances for Germany since breaking into the senior set-up last year.